"""
难度：中等
请你判断一个 9 x 9 的数独是否有效。只需要 根据以下规则 ，验证已经填入的数字是否有效即可。
数字 1-9 在每一行只能出现一次。
数字 1-9 在每一列只能出现一次。
数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。（请参考示例图）
注意：
一个有效的数独（部分已被填充）不一定是可解的。
只需要根据以上规则，验证已经填入的数字是否有效即可。
空白格用 '.' 表示。
示例 1：
输入：board = 
[["5","3",".",".","7",".",".",".","."]
,["6",".",".","1","9","5",".",".","."]
,[".","9","8",".",".",".",".","6","."]
,["8",".",".",".","6",".",".",".","3"]
,["4",".",".","8",".","3",".",".","1"]
,["7",".",".",".","2",".",".",".","6"]
,[".","6",".",".",".",".","2","8","."]
,[".",".",".","4","1","9",".",".","5"]
,[".",".",".",".","8",".",".","7","9"]]
输出：true
示例 2：
输入：board = 
[["8","3",".",".","7",".",".",".","."]
,["6",".",".","1","9","5",".",".","."]
,[".","9","8",".",".",".",".","6","."]
,["8",".",".",".","6",".",".",".","3"]
,["4",".",".","8",".","3",".",".","1"]
,["7",".",".",".","2",".",".",".","6"]
,[".","6",".",".",".",".","2","8","."]
,[".",".",".","4","1","9",".",".","5"]
,[".",".",".",".","8",".",".","7","9"]]
输出：false
解释：除了第一行的第一个数字从 5 改为 8 以外，空格内其他数字均与 示例1 相同。 但由于位于左上角的 3x3 宫内有两个 8 存在, 因此这个数独是无效的。"""


"""
判断数独有效，需要分别看每一行、每一列、每一个 3*3 的小方格是否出现了重复数字，如果都没有出现重复数字就是一个有效的数独，如果出现了重复数字则不是有效的数独。
考虑用 3 个 9*9 的数组分别来表示该数字是否在所在的行，所在的列，所在的方格出现过，如果出现了，就返回 false，遍历完没有出现，则返回 ture。
其中方格角标的计算用 box[(i/3)*3+(j/3)][n] 来表示。"""

class Solution:
    def isValidSudoku(self, board: List[List[str]]) -> bool:
        rows = [[0 for i in range(10)] for j in range(10)]
        columns = [[0 for i in range(10)] for j in range(10)]
        boxes = [[0 for i in range(10)] for j in range(10)]

        for i in range(9):
            for j in range(9):
                if board[i][j] != ".":
                    num = int(board[i][j])
                    box_index = (i//3 )* 3 + j // 3

                    if rows[i][num] > 0 or columns[j][num] >0 or  boxes[box_index][num] > 0:
                        return False
                    rows[i][num] = 1
                    columns[j][num] = 1

                    boxes[box_index][num] = 1
        return True



        

